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Conformal Symmetries of the Ricci Tensor for Certain Spacetimes

Thesis Info

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Author

Khan, Fawad

Program

PhD

Institute

University of Peshawar

City

Peshawar

Province

KPK

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/12802/1/Thesis.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725781797

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In this thesis, we have investigated conformal symmetries of the Ricci tensor, also known as conformal Ricci collineations (CRCs), for certain physically important spacetimes including kantowski-Sachs spacetimes, static spacetimes with maximal symmetric transverse spaces, non-static spherically symmetric spacetimes and locally rotationally symmetric Bianchi type I and V spacetimes. For each of these spacetimes, the CRC equations are solved in degenerate as well as non-degenerate cases. When the Ricci tensor is degenerate, it is observed that for all the above mentioned spacetimes, the Lie algebra of CRCs is in nite-dimensional. For non-degenerate Ricci tensor, it is shown that the spacetimes under consideration always admit anite-dimensional Lie algebra of CRCs. For Kantowski-Sachs and locally rotationally symmetric Bianchi type V metrics, we obtain 15-dimensional Lie algebras of CRCs, which is the maximum dimension of conformal algebra for a spacetime. In case of static spacetimes with maximal symmetric transverse spaces, the dimension of Lie algebra of CRCs turned out to be 6, 7 or 15. Similarly, it is observed that non-static spherically symmetric spacetimes may possess 5, 6 or 15 CRCs for non-degenerate Ricci tensor. Finally, the dimension of Lie algebra of CRCs for locally rotationally symmetric Bianchi type I spacetimes is shown to be 7- or 15-dimensional. For all the above mentioned spacetimes, the CRCs are found subject to some highly non-linear di erential constraints. In order to show that the classes of CRCs are non-empty, some examples of exact form of the corresponding metric satisfying these constraints are provided.
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حمد

نعت شریف

ہنجو روواں یار دی خاطر
اس مدنی سرکارؐ دی خاطر
قاصد بنے رسولؐ پیغمبر
سوہنے اس دربار دی خاطر
ظاہر ہویا جگ تے آ کے
رب سوہنے دل دار دی خاطر
نورِ محمد ظاہر ہویا
اس دنیا گلزار دی خاطر
روندے رہے وچ غار حرا دے
اس امت گنہگار دی خاطر
دشمن دا وی پچھنا کردے
ٹُر گئے گھر بیمار دی خاطر
یار بلایا عرشاں اُتّے
اپنے خاص پیار دی خاطر
سجدے وچوں سر نہ چایا
اس حسینؑ سوار دی خاطر

 

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